Part 1 - AL-Tax

International Taxation Handbooka gross return equal to that in equation (2.5). Therefore, the pre-tax rate of returnon the project is equal to the cost of capital less economic depreciation, p C δ:(1 Ap )( ρδπδ ) .1 τ(2.7)Considering now the post-tax real rate of return for the investor, this is equal to:s (1 m)(r π) πw p , (2.8)where m is the marginal personal tax rate on interest income, r is the real rate ofinterest, π is the rate of inflation and w p is the marginal personal tax rate on wealth.The standard depreciation allowances, immediate expensing or free depreciationand tax credits (A), first stated in equation (2.4), can be expressed as:A f 1 A d f 2 τ f 3 g, (2.9)where f 1 is the proportion of the cost of an asset subject to the standard depreciationallowances (A d ), f 2 is the proportion of the cost qualifying for immediateexpensing at corporate tax rate τ, and f 3 denotes the proportion qualifying for grantsat the rate of grant g. The exact form of this expression depends on the provisionsof the tax code. Considering only that the present value of standard allowancesdepends upon the pattern of tax depreciation, several formulas are allowed in thetax systems (declining balance, straight line, sum-of-the-years digits, etc.). 7 Forinstance, if depreciation is granted at a rate α on a declining balance basis on historicalcost:A aa tad τ e( ρπ )d t τ∫.0a ρπ From expression (2.9) we can derive the following well-known proposition.(2.10)Proposition 1 In the absence of personal taxes and with equity finance, if the taxcode allows for full immediate expensing of investment, the METR is equal to zero.Proof Under immediate expensing A τ, and replacing in equation (2.7), it followsimmediately that METR 0.Finally, King and Fullerton link the firm’s discount rate (ρ) with the market interestrate (i), depending upon the source of finance: Debt, new shares issues, andretained earnings. When choosing one of these sources, the firm will try to minimizeits financial cost (see Alworth, 1988, Chapter 5).18